Question: Solve for $x$ and $y$ using substitution. ${-x-y = 1}$ ${x = -3y-9}$
Answer: Since $x$ has already been solved for, substitute $-3y-9$ for $x$ in the first equation. ${-}{(-3y-9)}{- y = 1}$ Simplify and solve for $y$ $3y+9 - y = 1$ $2y+9 = 1$ $2y+9{-9} = 1{-9}$ $2y = -8$ $\dfrac{2y}{{2}} = \dfrac{-8}{{2}}$ ${y = -4}$ Now that you know ${y = -4}$ , plug it back into $\thinspace {x = -3y-9}\thinspace$ to find $x$ ${x = -3}{(-4)}{ - 9}$ $x = 12 - 9$ ${x = 3}$ You can also plug ${y = -4}$ into $\thinspace {-x-y = 1}\thinspace$ and get the same answer for $x$ : ${-x - }{(-4)}{= 1}$ ${x = 3}$